Ejection Dynamics of a Semi-flexible Polymer from a Nano-sphere

Abstract

Polymer ejection has been of interest due to its relation to the viral genome ejection. However, the ejection dynamics of a semi-flexible polymer from a nano-sphere is not yet understood. Here, a theory is developed for the ejection dynamics of a polymer with total length $L_0$ and persistence length $l$ from a sphere of diameter $D$. These length-scales define different confinement regimes, to study the polymer dynamics. The polymer sometimes undergoes between two to three regimes, during its ejection. The rate of change of the free energy of confinement is balanced by the rate of energy dissipation, in each regime. The polymer experiences a final stage in which the free energy of polymer attachment to the sphere governs the ejection. The total ejection time $\tau$ depends on the polymer dynamics in the various regimes that it passes through in the phase-space. Dependence of the ejection time on the polymer length, the persistence length and the sphere diameter $\tau \propto L_0^{\alpha}D^{\beta}l^{\gamma}$ is obtained from the theory. It is shown that $\alpha$ changes between 1 and 1.7, $\beta$ between 3 and 5, and $\gamma$ takes a zero or positive value often smaller than 1. Agreement of these exponents with other theory and simulations are discussed.